A Brain Teaser

A man is sitting in a pub feeling rather poor. He sees the man next to him pull a wad of £50 notes out of his wallet. He turns to the rich man and says to him, "I have an amazing talent; I know almost every song that has ever existed."
The rich man laughs.
The poor man says, "I am willing to bet you all the money you have in your wallet that I can sing a genuine song with a lady's name of your choice in it."
The rich man laughs again and says,
"OK, how about my daughter's name,
Joanna Armstrong-Miller?"

The rich man goes home poorer!
The poor man goes home richer!
What song did he sing?